Circumradii of equilateral and isosceles triangles

First, have students derive the formula for the circumradius of an equilateral triangle, with sides of length \(s.\) The correct formula is \(s / \sqrt{3}.\) After that, have students derive the formula for the circumradius of an isosceles triangle, with base \(b,\) height \(h,\) and slant height \(s.\) The correct formula is \(r = s^2 / (2h).\) Its derivation can be seen here.

Concude by giving your students this challenge:

Roll These Dice by NRICH: If students are successful, try generalizing the problem to \(r\) red dice and \(g\) green dice. That is, have students make a table, with columns "number of red dice," "number of green dice," "smallest possible answer," and "largest possible answer."